Context. The quest for the cosmological parameters that describe our universe continues to motivate the scientific community to undertake very large survey initiatives across the electromagnetic spectrum. Over the past two decades, the Chandra and XMM-Newton observatories have supported numerous studies of X-ray-selected clusters of galaxies, active galactic nuclei (AGNs), and the X-ray background. The present paper is the first in a series reporting results of the XXL-XMM survey ; it comes at a time when the Planck mission results are being finalised. Aims: We present the XXL Survey, the largest XMM programme totaling some 6.9 Ms to date and involving an international consortium of roughly 100 members. The XXL Survey covers two extragalactic areas of 25 deg2 each at a point- source sensitivity of ~5 × 10-15 erg s-1 cm-2 in the [0.5-2] keV band (completeness limit). The survey's main goals are to provide constraints on the dark energy equation of state from the space-time distribution of clusters of galaxies and to serve as a pathfinder for future, wide-area X-ray missions. We review science objectives, including cluster studies, AGN evolution, and large-scale structure, that are being conducted with the support of approximately 30 follow-up programmes. Methods: We describe the 542 XMM observations along with the associated multi-λ and numerical simulation programmes. We give a detailed account of the X-ray processing steps and describe innovative tools being developed for the cosmological analysis. Results: The paper provides a thorough evaluation of the X- ray data, including quality controls, photon statistics, exposure and background maps, and sky coverage. Source catalogue construction and multi-λ associations are briefly described. This material will be the basis for the calculation of the cluster and AGN selection functions, critical elements of the cosmological and science analyses. Conclusions: The XXL multi-λ data set will have a unique lasting legacy value for cosmological and extragalactic studies and will serve as a calibration resource for future dark energy studies with clusters and other X-ray selected sources. With the present article, we release the XMM XXL photon and smoothed images along with the corresponding exposure maps.